Patrick Stevens

Wherein I detail the most beautiful proof of a theorem I’ve ever seen, in a bite-size form suitable for an Anki deck. I attach the Anki deck, which contains the bulleted lines of this post as flashcards.

Statement

There’s no particularly nice way to motivate this in this context, I’m afraid, so we’ll just dive in. I have found this method extremely hard to motivate - a few of the steps are a glorious magic.

is a sum of two squares iff in the prime factorisation of , primes 3 mod 4 appear only to even powers.